In so-called full second-order logic, the second-order variables range over all subsets and relations of the domain in question. In so-called Henkin second-order logic, every model is endowed with a set of subsets and relations which will serve as the range of the second-order variables. In our Boolean-valued second-order logic, the second-order variables range over all Boolean-valued subsets and relations on the domain. We show that under large cardinal assumptions Boolean-valued second-order logic is more robust than full second-order logic. Its validity is absolute under forcing, and its Hanf and Löwenheim numbers are smaller than those of full second-order logic.
|Number of pages||24|
|Journal||Notre Dame Journal of Formal Logic|
|Publication status||Published - 2015|
- Boolean validity
- Boolean-valued second-order logic
- Full second-order logic
ASJC Scopus subject areas